Within one drawing my attempts to copy the contents of a layer
using copy/paste have failed. The paste shows the contents till I
click (left mouse) on the target site in the newly selected (empty) layer
and then the newly selected layer is apparently still blank.

1. Create a Layer you want. Right side, Add Layer.
2. Select the things you want to copy to this layer.
3. use hotkey "at" Atribute or "pr" Properties to Move the "selected things" to a given Layer.
4. done. Do checking by clicking the aye on the Layer List.